We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB. This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive enough to model multi-hop inferences, and scalable enough to use with realistically large KBs. The sparse-matrix reified KB can be distributed across multiple GPUs, can scale to tens of millions of entities and facts, and is orders of magnitude faster than naive sparse-matrix implementations. The reified KB enables very simple end-to-end architectures to obtain competitive performance on several benchmarks representing two families of tasks: KB completion, and learning semantic parsers from denotations.

We introduce a new operation which can be used to compositionally construct second-order multi-hop templates in a neural model, and evaluate a number of alternative implementations, with different time and memory trade offs. These techniques scale to KBs with millions of entities and tens of millions of triples, and lead to simple models with competitive performance on several learning tasks requiring multi-hop reasoning.